A Relation-Algebraic Approach to Liveness of Place/Transition Nets

Authors:
Alexander Fronk;Rudolf Berghammer
Affiliations:
MATERNA GmbH, Dortmund, Germany 44141;Christian-Albrechts-Universität Kiel, Kiel, Germany 24098
Venue:
RelMiCS '09/AKA '09 Proceedings of the 11th International Conference on Relational Methods in Computer Science and 6th International Conference on Applications of Kleene Algebra: Relations and Kleene Algebra in Computer Science
Year:
2009

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Abstract

We provide a relation-algebraic characterization of liveness in Petri nets based on a relation-algebraic definition of both the structure and the state space of Petri nets. Such an approach, compared to the common ones that apply predicate logic and set theory, shifts the formalization to a more abstract level. As a main benefit, Petri net properties can be proved in a rigorous mathematical style. Since the characterizations are executable relational specifications, they provide the possibility for tool support.